Prime Number Diffeomorphisms, Diophantine Equations and the Riemann Hypothesis

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dc.creatorAlexandrov, Lubomir
dc.creatorGeorgiev, Lachezar
dc.date2004-11-22
dc.date.accessioned2026-07-07T04:31:39Z
dc.date.available2026-07-07T04:31:39Z
dc.descriptionWe explicitly construct a diffeomorphic pair (p(x),p^{-1}(x)) in terms of an appropriate quadric spline interpolating the prime series. These continuously differentiable functions are the smooth analogs of the prime series and the prime counting function, respectively, and contain the basic information about the specific behavior of the primes. We employ p^{-1}(x) to find approximate solutions of Diophantine equations over the primes and discuss how this function could eventually be used to analyze the von Koch estimate for the error in the prime number theorem which is known to be equivalent to the Riemann hypothesis.
dc.description12 pages, 2 EPS figures
dc.identifierhttps://arxiv.org/abs/math-ph/0411071
dc.identifierhttp://arxiv.org/abs/math-ph/0411071
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57897
dc.subjectMathematical Physics
dc.titlePrime Number Diffeomorphisms, Diophantine Equations and the Riemann Hypothesis
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